Problem: Luis is 18 years younger than Omar. Omar and Luis first met 3 years ago. Seven years ago, Omar was 3 times older than Luis. How old is Omar now?
Explanation: We can use the given information to write down two equations that describe the ages of Omar and Luis. Let Omar's current age be $o$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $o = l + 18$ Seven years ago, Omar was $o - 7$ years old, and Luis was $l - 7$ years old. The information in the second sentence can be expressed in the following equation: $o - 7 = 3(l - 7)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = o - 18$ . Substituting this into our second equation, we get the equation: $o - 7 = 3($ $(o - 18)$ $ -$ $ 7)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 7 = 3o - 75$ Solving for $o$ , we get: $2 o = 68$ $o = 34$.